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Apr 18, 2008 - arXiv:0804.2624v2 [cond-mat.str-el] 18 Apr 2008 draft. Magneto-transport properties governed by the antiferromagnetic fluctuations in heavy.
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Magneto-transport properties governed by the antiferromagnetic fluctuations in heavy fermion superconductor CeIrIn5 Y. Nakajima,1,2,∗ H. Shishido,1 H. Nakai,1 T. Shibauchi,1 M. Hedo,2,† Y. Uwatoko,2 T. Matsumoto,3 R. Settai,4 Y. Onuki,4 H. Kontani,5 and Y. Matsuda1,2 1

arXiv:0804.2624v2 [cond-mat.str-el] 18 Apr 2008

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Department of Physics, Kyoto University, Kyoto 606-8502, Japan Institute for Solid State Physics, University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8581, Japan 3 National Institute of Material Science, Sakura, Tsukuba, Ibaraki 305-0003, Japan 4 Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan and 5 Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan In quasi-two dimensional Ce(Ir,Rh)In5 system, it has been suggested that the phase diagram contains two distinct domes with different heavy fermion superconducting states. We here report the systematic pressure dependence of the electron transport properties in the normal state of CeRh0.2 Ir0.8 In5 and CeIrIn5 , which locates in first and second superconducting dome, respectively. We observed non-Fermi liquid behavior at low temperatures in both compounds, including non-quadratic T −dependence of the resistivity, large enhancement of the Hall coefficient, and the violation of the Kohler’s rule in the magnetoresistance. We show that the cotangent of Hall angle cot ΘH varies as T 2 , and the magnetoresistance is quite well scaled by the Hall angle as ∆ρxx /ρxx ∝ tan2 ΘH . The observed transport anomalies are common features of CeM In5 (M =Co, Rh, and Ir) and high-Tc cuprates, suggesting that the anomalous transport properties observed in CeIrIn5 are mainly governed by the antiferromagnetic spin fluctuations, not by the Ce-valence fluctuations which has been proposed to be the possible origin for the second superconducting dome. PACS numbers: 71.27.+a,74.25.Fy,74.25.Dw,74.70.Tx

I.

INTRODUCTION

The resent discoveries of heavy fermion compounds CeM In5 (M =Rh, Co, and Ir) give a unique opportunity to elucidate the interplay between the magnetism and the superconductivity. The ground state of these compounds can be tuned by pressure and chemical doping. CeCoIn5 1 and CeIrIn5 2 are superconductors with the transition temperature Tc = 2.3 K and 0.4 K at ambient pressure, respectively. On the other hand, CeRhIn5 is an antiferromagnet with TN = 3.8 K at ambient pressure and shows superconductivity under pressure.3 In CeCoIn5 and CeRhIn5 , the thermodynamic and transport properties in the normal state exhibit a striking deviation from conventional Fermi liquid behavior,4,5,6 which is commonly observed in the systems in the vicinity of the antiferromagnetic (AF) quantum critical point (QCP). Then it is widely believed that the superconductivity in CeRhIn5 and CeCoIn5 is closely related to the AF fluctuations. Recently, it has been suggested that CeIrIn5 should be distinguished from CeCoIn5 and CeRhIn5 , although all three compounds share similar quasi-two dimensional (2D) band structure.7,8 Figure 1 depicts the schematic temperature – x (T -x) phase diagram of CeRh1−x Irx In5 and temperature – pressure (T -P ) phase diagram of CeIrIn5 .9,10 In this system the Rh substitution for Ir increases the c/a ratio, acting as a negative chemical pressure that increases AF correlations. In CeRh1−x Irx In5 , the ground state continuously evolves from AF metal (x < 0.5) to superconductivity (x > 0.5). Tc shows a maximum at x ∼ 0.7 and exhibits a cusp-like minimum at x ∼ 0.9, forming a first dome (SC1). The

superconductivity nature in SC1, which occurs in the proximity to AF QCP, should be essentially the same as CeCo(In1−x Cdx )5 12 and CeRhIn5 .3 The strong AF fluctuations associated with the AF QCP nearby are observed in SC1.10,13 In CeIrIn5 (x = 1), Tc increases with pressure and exhibits a maximum (Tc = 1 K) at P ∼ 3 GPa, forming a second dome (SC2). The AF fluctuations in SC2 far from the AF QCP are strongly suppressed, compared with those in SC1.10,13,14 Moreover, it has been reported that the nature of the crossover behavior from non-Fermi to Fermi liquid in strong magnetic fields for CeIrIn5 is very different from that for CeCoIn5 and CeRhIn5 .15,16,17 From the analogy to CeCu2 (Si1−x Gex )2 with two distinct superconducting domes,18 a possibility that the Cevalence fluctuations play an important role for the normal and superconducting properties in CeIrIn5 has been pointed out.19 For instance, it has been suggested that while the superconductivity in SC1 is magnetically mediated, the superconductivity in SC2 may be mediated by the Ce-valence fluctuations.20 Thus the major outstanding question is whether the Ce-valence fluctuations play an important role for the physical properties of CeIrIn5 in SC2 phase. Our previous studies indicate that the transport coefficients, including resistivity, Hall effect, and magnetoresistance, can be powerful tools to probe the AF spin fluctuations.21,22,23 In this paper, we report the systematic pressure study of the transport properties for CeRh0.2 Ir0.8 In5 and CeIrIn5 , which locates in SC1 and SC2 phase, respectively. We provide several pieces of evidence that all the anomalous transport properties observed in CeIrIn5 and CeRh0.2 Ir0.8 In5 originate from the AF spin fluctuations irrespective of which supercon-

2 of ρxx for CeIrIn5 and CeRh0.2 Ir0.8 In5 , respectively. The resistivities of CeIrIn5 and CeRh0.2 Ir0.8 In5 are markedly different from the T 2 -behavior expected in Fermi liquid metals. At ambient pressure, ρxx varies as ρxx ∼ T α

(1)

with α ∼ 1 for CeIrIn5 and ∼ 0.7 for CeRh0.2 Ir0.8 In5 . α increases with pressure for both systems and reaches ∼ 1.4 at 2.4 GPa for CeIrIn5 and ∼ 1.3 at 2.19 GPa

FIG. 1: Schematic T -x phase diagram for CeRh1−x Irx In5 and T -P phase diagram for CeIrIn5 9,10,11 .

ducting phase the system belongs to.

II.

EXPERIMENTAL

The high quality single crystals of CeIrIn5 and CeRh0.2 Ir0.8 In5 were grown by the self-flux method. We performed all measurements on samples with a typical dimension of ∼ 1.0×2.0×0.1 mm3 in the transverse geometry for H k c and the current J k a. The Hall effect and transverse magnetoresistance were measured simultaneously. We obtained Hall resistivity from the transverse resistance by subtracting the positive and negative magnetic field data. Hydrostatic pressure up to 2.41 GPa were generated in a piston-cylinder type high pressure cell with oil as a transmitting fluid (Daphne 7373 : petroleum ether = 1 : 1). The pressure inside the cell was determined by the superconducting transition temperature of Pb.

III.

RESULTS

A.

Resistivity

Figures 2(a) and (b) show the temperature dependence of the resistivity ρxx in zero field at several pressures for CeIrIn5 and CeRh0.2 Ir0.8 In5 , respectively. The overall feature of the temperature dependence for both compounds is typical in Ce-based heavy fermion compounds. On cooling from room temperature, ρxx first decreases and then increases due to dominant Kondo scattering. At lower temperatures, ρxx exhibits a metallic behavior after showing a broad maximum at around the temperature Tcoh , shown by arrows. Tcoh corresponds to the Fermi temperature of f electrons and the system becomes coherent below Tcoh . Tcoh increases with pressure. The insets of Figs. 2(a) and (b) show the low temperature data

FIG. 2: (a) Temperature dependence of resistivity for CeIrIn5 at 0, 0.56, 0.98, 1.59, and 2.41GPa. (b) Temperature dependence of resistivity for CeRh0.2 Ir0.8 In5 at 0, 0.49, 1.11, 1.50, and 2.19GPa. Insets are expanded views at low temperatures. Downarrows drawn in main panels indicate Tcoh at ambient pressure, where the resistivity shows a broad maximum. Open circles shown in the insets indicate the resistivity at Tm where RH shows a minimum. For detail, see the text in §.4.

3 for CeRh0.2 Ir0.8 In5 , indicating that the Fermi liquid behavior is recovering by applying pressure. We note that these α-value is close to that reported in Ref. 24. These temperature and pressure dependence of resistivities for CeIrIn5 and CeRh0.2 Ir0.8 In5 are very similar to those of CeCoIn5 and CeRhIn5 .22,23

B.

Hall effect

Figures 3 depict the Hall resistivity ρxy as a function of magnetic field at ambient pressure for CeIrIn5 . The sign of ρxy is negative. At low temperatures, ρxy deviates from the H-linear dependence. Similar behavior is observed in CeRh0.2 Ir0.8 In5 . Figures 4(a) and (b) show the temperature dependence of the Hall coefficient RH in dρxy at several zero field limit defined as RH ≡ limH→0 dH pressures for CeIrIn5 and CeRh0.2 Ir0.8 In5 , respectively. For comparison, RH of LaIrIn5 , which has no f -electron and has similar band structure to CeIrIn5 , is plotted in the same figure. For LaIrIn5 , RH shows a shallow minimum at around 20 K and becomes nearly T -independent at low temperatures. The carrier number estimated from RH ∼ 3 × 10−10 m3 /C for LaIrIn5 at low temperatures corresponds to nearly three electrons per unit cell, which is consistent with the number expected from the band structure, indicating RH ≃ 1/ne where n is the carrier number. The Hall effect in CeIrIn5 and CeRh0.2 Ir0.8 In5 is distinctly different from that in LaIrIn5 . The temperature dependence of RH for CeIrIn5 and CeRh0.2 Ir0.8 In5 is closely correlated with the resistivity. The down-arrow in Figs. 4 (a) and (b) indicates Tcoh at ambient pressure determined by the resistivity peak in Figs. 2(a) and (b), respectively. In the high temperature regime above Tcoh , RH for CeIrIn5 and CeRh0.2 Ir0.8 In5 shows weak T dependence. Well above Tcoh , RH for both compounds well coincides with RH of LaIrIn5 , indicating RH ≃ 1/ne. Below Tcoh , RH for CeIrIn5 and CeRh0.2 Ir0.8 In5 decreases rapidly with decreasing T . At lower temperatures, RH increases after showing minimum at Tm indi-

FIG. 3: Field dependence of ρxy for CeIrIn5 at ambient pressure.

FIG. 4: (a) Temperature dependence of RH for CeIrIn5 at several pressures (0 (•), 0.56 (), 0.98 (N), 1.56 (), and 2.41 GPa (H)) and for LaIrIn5 at ambient pressure (◦). RH is defined by the zero-field limit for derivative of ρxy . Inset: Temperature dependence of RH for CeIrIn5 at 0 (•), 1 (+), and 5 T (×) at ambient pressure. (b)Temperature dependence of RH for CeRh0.2 Ir0.8 In5 at several pressures (0 (•), 0.49 (), 1.11 (N), 1.50 () and 2.19 GPa (H)) and for LaIrIn5 at ambient pressure (◦). Inset: Temperature dependence of RH for CeRh0.2 Ir0.8 In5 at 0 (•), 1 (+), and 5 T (×) at ambient pressure. Down and up arrows in main panels indicate Tcoh at ambient pressure determined by the resistivity peak and Tm at ambient pressure, where RH shows a minimum, respectively.

cated by up-arrows in Figs. 4(a) and (b). With increasing pressure, Tm increases and the enhancement of |RH | at low temperature regime is reduced for CeIrIn5 . The insets of Figs. 4 (a) and (b) show the temperature dependence of RH at µ0 H=0, 1, and 5 T at ambient pressure for CeIrIn5 and CeRh0.2 Ir0.8 In5 , respectively. RH is defined by a field derivative of ρxy , RH ≡ dρxy /dH. The magnitude of RH below Tcoh is strongly suppressed by

4 of T 2 for CeIrIn5 . In the all pressure regime, cot ΘH well obeys a T 2 -dependence, except for the low temperature regime, exhibiting a striking similarity with CeCoIn5 and CeRhIn5 , and high-Tc cuprates. C.

FIG. 5: | cot ΘH | as a function of (T /Tcoh )2 for CeIrIn5 at 0 (•), 0.56 (◦), 0.98 (), 1.59 (), and 2.41 GPa (N).

magnetic fields. We here comment on the effect of the skew scattering. Usually, RH in heavy fermion compounds can be n written by the sum of the ordinary Hall part RH due to a Lorentz force and the anomalous Hall part RH due to skew scattering,25 n a RH = RH + RH .

(2)

a The magnitude of RH is often much larger than that of n RH except for T ≪ Tcoh and T ≫ Tcoh . In most Cea based heavy fermion systems, RH is positive in sign and shows a strong T -dependence, which is scaled by χρxx a (Ref. 25) or χ.26 At around Tcoh , RH shows a broad maximum and its amplitude becomes much larger than 1/|ne|. It it obvious that RH of CeIrIn5 and CeRh0.2 Ir0.8 In5 are very different from that expected from the skew scattering. In fact, the sign of RH is negative in the whole temperature regime. Moreover, RH is close to 1/ne at T ∼ Tcoh . A slight increase of RH observed at T & Tcoh in the low pressure regime appears to come from small but finite contribution of the skew scattering. Thus the skew scattering contribution is small in CeIrIn5 and CeRh0.2 Ir0.8 In5 and the normal part of Hall effect is dominant. We also note that skew scattering is negligibly small in CeRhIn5 and CeCoIn5 .21,22,23 The Hall effect in CeIrIn5 and CeRh0.2 Ir0.8 In5 below Tcoh , particularly the enhancement of |RH | from |1/ne|, is distinctly different from that expected in the conventional metals. Such an enhancement has also been reported in CeCoIn5 and CeRhIn5 , and high-Tc cuprates. There, it has been shown that the Hall problem can be simplified when analyzed in terms of Hall angle ΘH ≡ ρxy tan−1 ρxx ; cot ΘH well obeys a T 2 -dependence,

cot ΘH = AT 2 + B,

Magnetoresistance

Figures 6 (a) and (b) show the magnetoresistance ∆ρxx /ρxx (0) ≡ (ρxx (H) − ρxx (0))/ρxx (0) of CeIrIn5 at ambient pressure and at P = 2.41 GPa, respectively. The magnetoresistance varies as ∆ρxx /ρxx (0) ∝ H 2 at very low field (µ0 H < 0.2 T). At ambient pressure, the magnetoresistance decreases with H at high fields below 5 K. This phenomena has also been observed in CeCoIn5 at ambient pressure21,23 and is attributed to the spin-flop scattering. We here discuss the magnetoresistance in the conventional and unconventional metals. In conventional metals, the magnetoresistance due to orbital motion of carriers obeys the Kohler’s rule,   ∆ρxx (H) µ0 H , (4) =F ρxx (0) ρxx (0) where F (x) is a function which depends on the details of electronic structure.30 It has been shown that the magnetoresistance in LaRhIn5 with similar electronic structure but with weak electronic correlation well obeys the Kohler’s rule.23 We first test the validity of the Kohler’s rule in the magnetoresistance of CeIrIn5 . Figures 7(a)

(3)

where A and B are constants.27,28,29 We here examine cot ΘH for CeIrIn5 . Figure 5 depicts cot ΘH as a function

FIG. 6: Magnetoresistance of CeIrIn5 as a function of H at (a) 0 GPa and (b) 2.41 GPa.

5 (i) The dc-resistivity shows non-quadratic dependence, ρxx ∝ T α with α close to unity at ambient pressure. (ii) |RH | increases with decreasing temperature and reaches a value much larger than |1/ne| well below Tcoh . The Hall angle varies as cot ΘH ∝ T 2 . (iii) Magnetoresistance displays T - and H- dependence that strongly violates the Kohler’s rule, ∆ρxx (H)/ρxx (0) 6= F (µ0 H/ρxx (0)). Magnetoresistance well obeys the modified Kohler’s rule that indicates a scaling by the the Hall angle, ∆ρxx /ρxx ∝ tan2 ΘH .

FIG. 7: Kohler’s plot. ∆ρxx /ρxx (0) vs µ0 H/ρxx (0) for CeIrIn5 at (a)0GPa, and (b)2.41GPa. Modified Kohler’s plot. ∆ρxx /ρxx (0) as a function of tan2 ΘH for CeIrIn5 at (c)0GPa and (d)2.41GPa.

and (b) depict ∆ρxx /ρxx (0) of CeIrIn5 as a function of µ0 H/ρxx (0) at 0 and 2.41 GPa, respectively. The data never collapse into the same curve, indicating a violation of the Kohler’s rule. A striking violation of the Kohler’s rule has been reported in CeCoIn5 and CeRhIn5 , and high-Tc cuprates. It has been shown instead that in these systems the magnetoresistance is well scaled by tan2 ΘH (modified Kohler’s rule), where ΘH ≡ tan−1 (ρxy /ρxx ) is the Hall angle;21,23,31 ∆ρxx ∝ tan2 ΘH . ρxx (0)

(5)

We then examine the validity of the modified Kohler’s rule for CeIrIn5 . In Figs. 7(c) and (d), the same data of magnetoresistance are plotted as a function of tan2 ΘH . For both cases, the data collapse into the same curve for three orders of magnitude, indicating that the magnetoresistance well obeys modified Kohler’s rule. The deviation from the modified Kohler’s rule is observed at low temperature and high field region, possibly due to the spin-flop scattering.

It should be emphasized that all of these features bear striking resemblance to those observed in CeCoIn5 , CeRhIn5 , and high-Tc cuprates. Therefore, it is natural to consider that the transport properties commonly observed in CeIrIn5 originate from the same mechanism. Our previous studies have shown that the anomalous features in the transport phenomena (i)–(iii) can be accounted for in terms of the recent theory in which the anisotropic inelastic scattering due to AF spin fluctuations are taken into account. In the presence of strong AF fluctuations, the transport scattering rate strongly depends on the position of the Fermi surface. Then the hot spots, at which the electron scattering rate is strongly enhanced by the AF fluctuations, appear at the positions where the AF Brilouin zone intersects with the Fermi surface. The presence of the hot spots has been confirmed in high-Tc cuprates and CeIn3 .32 Since the hot spot area does not contribute to the electron transport, it reduces the effective carrier density, which results in the enhancement of the |RH | from |1/ne|. In such a situation, various transport properties are determined by τcold , where τcold is the scattring time of the cold spots on the Fermi surface, at which the electrons are less scattered. Moreover, it has been shown that the transport properties are modified by the backflow accompanied with the anisotropic inelastic scattering.33,34,35,36 According to Refs. 33,34,35,36, the transport properties under magnetic fields are governed by the AF correlation length ξAF in the presence of backflow effect. Zerofield diagonal conductivity σxx (0), Hall conductivity σxy and magnetoconductivity ∆σxx (H) ≡ σxx (H) − σxx (0) are given as σxx (0) ∼ τcold ,

(6)

2 2 σxy ∼ ξAF τcold H,

(7)

4 3 ∆σxx ∼ ξAF τcold H 2.

(8)

and IV.

DISCUSSION

Summarizing the salient features in the transport properties of CeIrIn5 below Tcoh , which corresponds to the Fermi temperature of f electrons,

Here, we have dropped the higher terms with respect to τcold H since ∆ρ/ρ0 ≪ 1 in the present experiment, which suggests that the relation ωc τ ≪ 1 is satisfied. In the

6 2 presence of AF fluctuation, ξAF depends on T as ξAF ∝ 1/(T + θ), where θ is the Weiss temperature. Moreover, according to AF spin fluctuation theory, τcold is nearly inversely proportional to T ; τcold ∝ 1/T .33 When T ≫ θ, we then obtain the temperature dependence of the −1 2 resistivity, ρxx = σxx , Hall coefficient, RH = σxy /σxx H, and the Hall angle as −1 ρxx ∝ τcold ∝ T,

(9)

1 , T

(10)

2 RH ∝ ξAF ∝

and cot ΘH ∝ T 2 .

(11)

By definition, the magnetoresistance is given by  2 ∆ρxx (H) σxy (H) ∆σxx (H) =− − . ρxx (0) σxx (0) σxx (0)

(12)

−1 Using the relation ∆σxx (H)/σxy (H)2 ∼ τcold , given by Eqs. (7) and (8), the magnetoresistance is obtained as

∆ρxx (H) = (tan ΘH )2 · ρxx (0)



σxx (H) σxx (0)

2

· (C − 1),

(13)

where C is a constant and is ∼ 10-100 for CeM In5 . Since σxx (H)/σxx (0) ≃ 1 at low fields, ∆ρxx (H)/ρxx (0) is well scaled by tan2 ΘH . Thus Eqs. (9), (10), (11), and (13) reproduce the salient features of resistivity, Hall coefficient, Hall angle, and magnetoresistance observed in CeIrIn5 , respectively. The H-dependence of RH shown in the insets of Fig. 4(a) reinforces the conclusion that the AF fluctuations govern the electron transport phenomena in CeIrIn5 (also in CeRh0.2 Ir0.8 In5 ). The enhancement of |RH | below Tcoh is strongly suppressed by magnetic fields and approaches that of RH of LaIrIn5 . This is consistent with the recovery of the Fermi liquid state in magnetic fields in CeIrIn5 . Similar phenomena have also been reported in CeCoIn5 and CeRhIn5 , where the Fermi liquid state is recovered in magnetic fields by the suppression of AF fluctuations.23 The upturn behavior of RH for CeIrIn5 and CeRh0.2 Ir0.8 In5 at low temperatures below Tm shown in Figs. 4 (a) and (b) is also observed in CeCoIn5 .21,22,23 This phenomenon can be explained by the reduction of backflow effect due to the effect of the impurity scattering. Below Tm , isotropic impurity scattering becomes dominant and the backflow effect due to anisotropic scattering is relatively reduced.22,23 To obtain more insight into the impurity effect, we compare the resistivity values at Tm . The small open circles in the insets of Figs. 2 (a) and (b) indicate the resistivity at Tm where RH shows a minimum. The values of the resistivity at Tm are nearly pressure independent and close to ∼ 5 µΩcm and ∼ 8 µΩcm in CeIrIn5 and CeRh0.2 Ir0.8 In5 , respectively. We note

that these values are close to the values of ρxx at Tm for CeCoIn5 . We here discuss the difference between CeIrIn5 and CeCu2 (Si1−x Gex )2 . For CeCu2 (Si1−x Gex )2 in the second superconducting dome, anomalous behavior in transport and thermodynamic properties are observed near the pressure Pv , where Tc shows a maximum. For instance, α in Eq. (1) approaches unity and residual resistivity ρ0 exhibits a maximum near Pv .18 For CeIrIn5 , on the other hand, α approaches the Fermi liquid value at P ∼ 3 GPa, where Tc shows a maximum. Moreover, the residual resistivity decreases with pressure as shown in the insets of Fig. 2, which could be caused by the backflow or enhancement of impurity scattering near AF QCP.36 These results indicate that there seems to be crucial differences in the transport phenomena between CeIrIn5 and CeCu2 (Si1−x Gex )2 . The presence of the AF fluctuations in CeIrIn5 has been reported by the measurements of the nuclear magnetic resonance (NMR) relaxation rate T1−1 . According to NMR results, AF fluctuations are strongly suppressed with pressure and there is no indication of the AF fluctuations at P & 1 GPa.10 The present results indicate that the transport measurements are more sensitive to the AF fluctuations than NMR experiments. We finally comment on the superconducting gap structure in CeIrIn5 . Recent measurements of the anisotropy of the inter- and in-plane thermal conductivity for CeIrIn5 suggest a hybrid gap structure,37 whose symmetry is different from dx2 −y2 for CeCoIn5 (Refs. 38,39,40) and (most probably) for CeRhIn5 . However, very recent thermal conductivity measurements under rotated magnetic fields suggest that the superconducting gap structure for CeIrIn5 has dx2 −y2 symmetry,41 which implies that the AF spin fluctuations are important for the occurence of the superconductivity for CeIrIn5 , which is consistent with the present work.

V.

CONCLUSION

We have investigated the detailed electron transport properties by applying pressure in the normal state of CeRh0.2 Ir0.8 In5 and CeIrIn5 , which locates in the first and second superconducting dome, respectively. We observed striking non-Fermi liquid behaviors below Tcoh , including non-quadratic T −dependence of the resistivity, large enhancement of the Hall coefficient at low temperatures (|RH | ≫ 1/|ne|), and the violation of the Kohler’s rule in the magnetroresistance ∆ρxx (H)/ρxx 6= F (µ0 H/ρxx ). Moreover, we showed that the cotangent of Hall angle cot ΘH varies as T 2 , and the magnetoresistance is quite well scaled by the Hall angle as ∆ρxx /ρxx ∝ tan2 ΘH . These non-Fermi liquid properties, particularly the Hall effect, are suppressed by pressure and magnetic fields. The observed transport anomalies are common features of CeIrIn5 , CeCoIn5 , CeRhIn5 , and high-Tc cuprates. These results lead us to conclude

7 that the non-Fermi liquid behavior observed in the transport properties in CeIrIn5 originates not from the Cevalence fluctuations but from the low-lying excitation due to the AF fluctuations that still remain in the second dome away from the first dome in the proximity to the AF QCP.

by a Grant-in-Aid for Scientific Reserch from the Ministry of Education, Culture, Sports, Science and Technology.

Acknowledgment

We thank H. Ikeda, K. Miyake and S. Watanabe for stimulating discussions. This work was partly supported





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Present address: Department of Applied Physics, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan. Present address: Department of Physics, University of the Ryukyus, Nishihara, Okinawa 903-0213, Japan. C. Petrovic, P.G. Pagliuso, M.F. Hundley, R. Movshovic, J.L. Sarrao, J.D. Thompson, Z. Fisk and P. Monthoux, J. Phys. Condens. Matter 13 L337 (2001). C. Petrovic, R. Movshovich, M. Jaime, P.G. Pagliuso, M.F. Hundley, J.L. Sarrao, Z. Fisk and J.D. Thompson, Europhys. Lett. 53 354 (2001). H. Hegger, C. Petrovic, E.G. Moshopoulou, M.F. Hundley, J.L. Sarrao, Z. Fisk and J.D. Thompson, Phys. Rev. Lett. 84 4986 (2000). T. Tayama, A. Harita, T. Sakakibara, Y. Haga, H. Shishido, R. Settai and Y. Onuki, Phys. Rev. B 65, 180504(R) (2002). V. A. Sidorov, M. Nicklas, P.G. Pagliuso, J.L. Sarrao, Y. Bang, A.V. Balatsky and J.D. Thompson, Phys. Rev. Lett. 89, 157004 (2002). A. Bianchi, R. Movshovich, I. Vekhter, P.G. Pagliuso and J.L. Sarrao, Phys. Rev. Lett. 91 257001 (2003). Y. Haga, Y. Inada, H. Harima, K. Oikawa, M. Murakawa, H. Nakawaki, Y. Tokiwa, D. Aoki, H. Shishido, S. Ikeda, N. Watanabe, and Y. Onuki, J. Phys. Soc. Jpn. 63, 060503 (2001). R. Settai, T. Takeuchi, and Y. Onuki, J. Phys. Soc. Jpn. 76, 051003 (2007). M. Nicklas, V.A. Sidorov, H.A. Borges, P.G. Pagliuso, J.L. Sarrao, and J.D. Thompson, Phys. Rev. B 70 020505(R) (2004). S. Kawasaki, M. Yashima, Y. Mugino, H. Mukuda, Y. Kitaoka, H. Shishido, and Y. Onuki: Phys. Rev. Lett. 96 147001 (2006). The increase of Ir substitution by 0.1 corresponds to ∼ 0.4 GPa. See Figs. 2(b) and (c) in Y. Mugino, S. Kawasaki, M. Yashima, H. Mukuda, Y. Kitaoka, H. Shishido, and Y. Onuki, J. Mag. Mag. Mat. 310, 584 (2007). L. D. Pham, Tuson Park, S. Maquilon, J. D. Thompson, and Z. Fisk, Phys. Rev. Lett. 97, 056404 (2006). G. -q. Zheng, K. Tanabe, T. Mito, S. Kawasaki, Y. Kitaoka, D. Aoki, Y. Haga, and Y. Onuki, Phys. Rev. Lett. 86 , 4664 (2001) S. Kawasaki, G.-q. Zheng, H. Kan, Y. Kitaoka, H.Shishido, and Y. Onuki: Phys. Rev. Lett. 94 037007 (2005). C. Capan, A. Bianchi, F. Ronning, A. Lacerda, J. D.

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